That page shows only latest stuff, but you can hit on Next at the bottom, or the archive pages along the side. In general, a camera gets raw support and then at some later stage it gets tethering support. The D5500 got raw support in April 2015, but there's no later mention of D5500, which suggests no tethering yet.

Hello Katie! I figured out a work around for tethering from the Nikon D5500 into Lightroom! I was very frustrated with it not being supported as of yet as well! I shot a How to video to demonstrate. Check it out! Ramahn Jemahl - YouTube